Weak$^*$ dentability index of spaces $C([0,α])$

Hajek, Petr; Lancien, Gilles; Prochazka, Antonin

Weak$^*$ dentability index of spaces $C([0,α])$

Authors

Hajek, Petr

Lancien, Gilles

Prochazka, Antonin

Description

We compute the weak$^*$-dentability index of the spaces $C(K)$ where $K$ is a countable compact space. Namely ${Dz}(C([0,ω^{ω^α}])) = ω^{1+α+1}$, whenever $0\leα<ω_1$. More generally, ${Dz}(C(K))=ω^{1+α+1}$ if $K$ is a scattered compact whose height $η(K)$ satisfies $ω^α<η(K)\leq ω^{α+1}$ with an $α$ countable.